Mass is a basic physical property of matter. The mass of an atom or a molecule is referred to as the atomic mass. The atomic mass is used to find the average mass of elements and molecules and to solve stoichiometry problems.

Molar Mass The Elements Handbook at KnowledgeDoor Our table of molar masses has over 160 values covering 84 elements. Each value has a full citation identifying its source. The integrated unit conversion calculator can quickly convert a value to the units that you need. Atomic mass is measured in Atomic Mass Units (amu) which are scaled relative to carbon, 12 C, that is taken as a standard element with an atomic mass of 12. This isotope of carbon has 6 protons and 6 neutrons. Thus, each proton and neutron has a mass of about 1 amu.

Introduction

In chemistry, there are many different concepts of mass. It is often assumed that atomic mass is the mass of an atom indicated in unified atomic mass units(u). However, the book Quantities, Units and Symbols in Physical Chemistry published by the IUPAC clearly states:

The name 'atomic mass' is used for historical reasons, and originates from the fact that chemistry was the first science to investigate the same physical objects on macroscopic and microscopic levels. In addition, the situation is rendered more complicated by the isotopic distribution. On the macroscopic level, most mass measurements of pure substances refer to a mixture of isotopes. This means that from a physical stand point, these mixtures are not pure. For example, the macroscopic mass of oxygen (O₂) does not correspond to the microscopic mass of O₂. The former usually implies a certain isotopic distribution, whereas the latter usually refers to the most common isotope (¹⁶O₂). Note that the former is now often referred to as the 'molecular weight' or 'atomic weight'.

These concepts are further explained below.

Average Mass

Isotopes are atoms with the same atomic number, but different mass numbers. A different mass size is due to the difference in the number of neutrons that an atom contains. Although mass numbers are whole numbers, the actual masses of individual atoms are never whole numbers (except for carbon-12, by definition). This explains how lithium can have an atomic mass of 6.941 Da. The atomic masses on the periodic table take these isotopes into account, weighing them based on their abundance in nature; more weight is given to the isotopes that occur most frequently in nature. Average mass of the element E is defined as:

[ m(E) = sum_{n=1} m(I_n) times p(I_n) ]

where ∑ represents a n-times summation over all isotopes (I_n) of element E, and p(I) represents the relative abundance of the isotope I.

Example 1

Find the average atomic mass of boron using the Table 1 below:

Mass and abundance of Boron isotopes

Solution

The average mass of Boron is:

[ m(B) = (10.013 Da)(0.199) + (11.009 Da)(0.801) = 1.99 Da + 8.82 Da = 10.81 Da ]

Relative Mass

Traditionally it was common practice in chemistry to avoid using any units when indicating atomic masses (e.g. masses on microscopic scale). Even today, it is common to hear a chemist say, '¹²C has exactly mass 12'. However, because mass is not a dimensionless quantity, it is clear that a mass indication needs a unit. Chemists have tried to rationalize the omission of a unit; the result is the concept of relative mass, which strictly speaking is not even a mass but a ratio of two masses. Rather than using a unit, these chemists claim to indicate the ratio of the mass they want to indicate and the atomic mass constant m_u which is defined analogous to the unit they want to avoid. Hence the relative atomic mass of the mass m is defined as:

[A_r = dfrac{m}{m_u} ]

The quantity is now dimensionless. As this unit is confusing and against the standards of modern metrology, the use of relative mass is discouraged.

Molecular Weight, Atomic Weight, Weight vs. Mass

Until recently, the concept of mass was not clearly distinguished from the concept of weight. In colloquial language this is still the case. Many people indicate their 'weight' when they actually mean their mass. Mass is a fundamental property of objects, whereas weight is a force. Weight is the force F exerted on a mass m by a gravitational field. The exact definition of the weight is controversial. The weight of a person is different on ground than on a plane. Strictly speaking, weight even changes with location on earth.

When discussing atoms and molecules, the mass of a molecule is often referred to as the 'molecular weight'. There is no univerally-accepted definition of this term; however, mosts chemists agree that it means an average mass, and many consider it dimensionless. This would make 'molecular weight' a synonym to 'average relative mass'.

Integer Mass

Because the proton and the neutron have similar mass, and the electron has a very small mass compared to the former, most molecules have a mass that is close to an integer value when measured in daltons. Therefore it is quite common to only indicate the integer mass of molecules. Integer mass is only meaningful when using dalton (or u) units.

Accurate Mass

Many mass spectrometers can determine the mass of a molecule with accuracy exceeding that of the integer mass. This measurement is therefore called the accurate mass of the molecule. Isotopes (and hence molecules) have atomic masses that are not integer masses due to a mass defect caused by binding energy in the nucleus.

Units

The atomic mass is usually measured in the units unified atomic mass unit (u), or dalton (Da). Both units are derived from the carbon-12 isotope, as 12 u is the exact atomic mass of that isotope. So 1 u is 1/12 of the mass of a carbon-12 isotope:

1 u = 1 Da = m(¹²C)/12

The first scientists to measure atomic mass were John Dalton (between 1803 and 1805) and Jons Jacoband Berzelius (between 1808 and 1826). Early atomic mass theory was proposed by the English chemist William Prout in a series of published papers in 1815 and 1816. Known was Prout's Law, Prout suggested that the known elements had atomic weights that were whole number multiples of the atomic mass of hydrogen. Berzelius demonstrated that this is not always the case by showing that chlorine (Cl) has a mass of 35.45, which is not a whole number multiple of hydrogen's mass.

Some chemists use the atomic mass unit (amu). The amu was defined differently by physicists and by chemists:

• Physics: 1 amu = m(¹⁶O)/16
• Chemistry: 1 amu = m(O)/16

Chemists used oxygen in the naturally occurring isotopic distribution as the reference. Because the isotopic distribution in nature can change, this definition is a moving target. Therefore, both communities agreed to the compromise of using m(¹²C)/12 as the new unit, naming it the 'unified atomic mass unit' (u). Hence, the amu is no longer in use; those who still use it do so with the definition of the u in mind. For this reason, the dalton (Da) is increasingly recommended as the accurate mass unit.

Neither u nor Da are SI units, but both are recognized by the SI.

Molar Mass

The molar mass is the mass of one mole of substance, whether the substance is an element or a compound. A mole of substance is equal to Avogadro's number (6.023×10²³) of that substance. The molar mass has units of g/mol or kg/mol. When using the unit g/mol, the numerical value of the molar mass of a molecule is the same as its average mass in daltons:

• Average mass of C: 12.011 Da
• Molar mass of C: 12.011 g/mol

This allows for a smooth transition from the microscopic world, where mass is measured in daltons, to the macroscopic world, where mass is measured in kilograms.

Example 2

What is the molar mass of phenol, C₆H₅OH?

Average mass m = 6 × 12.011 Da + 6 × 1.008 Da + 1 × 15.999 Da = 94.113 Da

Molar mass = 94.113 g/mol = 0.094113 kg/mo

Measuring Masses in the Atomic Scale

Masses of atoms and molecules are measured by mass spectrometry. Mass spectrometry is a technique that measures the mass-to-charge ratio (m/q) of ions. It requires that all molecules and atoms to be measured be ionized. The ions are then separated in a mass analyzer according to their mass-to-charge ratio. The charge of the measured ion can then be determined, because it is a multiple of the elementary charge. The the ion's mass can be deduced. The average masses indicated in the periodic table are then calculated using the isotopic abundances, as explained above.

The masses of all isotopes have been measured with very high accuracy. Therefore, it is much simpler and more accurate to calculate the mass of a molecule of interest as a sum of its isotopes than measuring it with a commercial mass spectrometer.

Note that the same is not true on the nucleon scale. The mass of an isotope cannot be calculated accurately as the sum of its particles (given in the table below); this would ignore the mass defect caused by the binding energy of the nucleons, which is significant.

As shown in Table 2, the mass of an electron is relatively small; it contributes less than 1/1000 to the overall mass of the atom.

Where to Find Atomic Mass

The atomic mass found on the Periodic Table (below the element's name) is the average atomic mass. For example, for Lithium:

The red arrow indicates the atomic mass of lithium. As shown in Table 2 above and mathematically explained below, the masses of a protons and neutrons are about 1u. This, however, does not explain why lithium has an atomic mass of 6.941 Da where 6 Da is expected. This is true for all elements on the periodic table. The atomic mass for lithium is actually the average atomic mass of its isotopes. This is discussed further in the next section.

One particularly useful way of writing an isotope is as follows:

Applications

Applications Include:

1. Average Molecular Mass
2. Stoichiometry

Note: One particularly important relationship is illustrated by the fact that an atomic mass unit is equal to 1.66 × 10^-24 g. This is the reciprocal of Avogadro's constant, and it is no coincidence:

[dfrac{rm Atomic~Mass~(g)}{1 {rm g}} times dfrac{1 {rm mol}}{6.022 times 10^{23}} = dfrac{rm Mass~(g)}{1 {rm atom}}]

Because a mol can also be expressed as gram × atoms,

[1 u = frac{M_u (molar mass unit)}{N_A (Avogadro's Number)} = 1 frac{g}{mol N_A} ]

1u = M_u(molar mass unit)/N_A(Avogadro's Number)=1g/mol/N_A

N_A known as Avogadro's number (Avogadro's constant) is equal to 6.023×10²³ atoms.

Atomic mass is particularly important when dealing with stoichiometry.

Practice Problems

1. What is the molecular mass of radium bicarbonate, Ra(HCO₃)₂?
2. List the following, from least to greatest, in terms of their number of neutrons, and then atomic mass: ¹⁴N, ⁴²Cl, ²⁵Na, ¹⁰Be
3. A new element, Zenium, has 3 isotopes, ⁵⁹Ze, ⁶¹Ze, and ⁶⁷Ze, with abundances of 62%, 27%, and 11% respectively. What is the atomic mass of Zenium?
4. An isotope with a mass number of 55 has 5 more neutrons than protons. What element is it?
5. How much mass does 3.71 moles of Fluorine have?
6. How many grams are there in 4.3 × 10²² molecules of POCl₃?
7. How many moles are there in 23 grams of sodium carbonate?

Solutions

a) Molecular mass of Ra(HCO₃)₂

= 226 + 2(1.01 u + 12.01 u + (16.00 u)(3)) = 348 u or g/mol

b) Number of neutrons: ¹⁰Be, ¹⁴N, ²⁵Na, ⁴²Cl

Atomic Mass: ¹⁰Be, ¹⁴N, ²⁵Na, ⁴²Cl

Note: It is the same increasing order for both number of neutrons and atomic mass because more neutrons means more mass.

c) Atomic mass of Zenium:

(59 u)(0.62) + (61 u)(0.27) + (67 u)(0.11)

= 37 u + 16 u + 7.4 u

= 60.4 u or g/mol

d) Mn

e) (3.71 moles F₂)(19 × 2 g/mol F₂)

= (3.71 mol F₂)(38 g/mol F₂)

= 140 g F₂

f) (4.3 × 10²² molecules POCI₃)(1 mol/6.022 × 10²³ molecules POCI3)(30.97 + 16.00 + 35.45 x 3 g/mol POCI₃)

= (4.3 × 10²² molecules POCI₃)(mol/6.022 × 10²³ molecules POCI3)(153.32 g/mol POCI₃)

= 11 g POCI₃

g) (23 g Na₂CO₃)(1 mol/22.99 × 2 + 12.01 + 16.00 × 3 g Na₂CO₃)

= (23 g Na₂CO₃)(1 mol/105.99 g Na₂CO₃)

= (0.22 mol Na₂CO₃)

References

1. Petrucci, Ralph, William Harwood, Geoffrey Herring, and Jeffry Madura. General Chemistry. 9th ed. Upper Saddle River, New Jersey: Pearson Prentice Hall, 2007
2. Clifford C. Houk, Richard Post. Chemistry Concepts and Problems, a Self-Teaching Guide. 2nd ed. New York : Wiley, 1996.
3. David R. Lide. CRC Handbook of Chemistry and Physics. 87th ed. New York: CRC Press, 2006.
4. Loss, R.D., Report of the IUPAC Commission on Atomic Weights and Isotopic Abundances, Chemistry International, 23, 179, 2001.
5. Mascetta, Joseph A. Chemistry The Easy Way. 3rd ed. New York: Barron's Educational Series, 1996.

Contributors and Attributions

• Gunitika Dandona (UCD)

Learning Objective

• To calculate the molecular mass of a covalent compound and the formula mass of an ionic compound and to calculate the number of atoms, molecules, or formula units in a sample of a substance.

Chemistry is the study of how atoms and molecules interact with each other which occurs on the atomic scale. Chemists need a way of simply determining how many molecules they have in a beaker. The mole concept, which we will introduce here, bridges that gap by relating the mass of a single atom or molecule in amu to the mass of a collection of a large number of such molecules in grams.

As you learned, the mass number is the sum of the numbers of protons and neutrons present in the nucleus of an atom. The mass number is an integer that is approximately equal to the numerical value of the atomic mass. Although the atomic mass is unitless, it is assigned units called atomic mass units (amu) measured relative to the mass of a single atom of ¹²C. Because a molecule or a polyatomic ion is an assembly of atoms whose identities are given in its molecular or ionic formula, we can calculate the average atomic mass of any molecule or polyatomic ion from its composition by adding together the masses of the constituent atoms. The average mass of a monatomic ion is the same as the average mass of an atom of the element because the mass of electrons is so small that it is insignificant in most calculations. This is not much help in the laboratory for the typical chemist who only has a balance to weight out chemicals but needs to know how the number of atoms or molecules. Clearly something clever is needed but first let us briefly review how to calculate molecular masses.

Molecular

The molecular mass The sum of the average masses of the atoms in one molecule of a substance, each multiplied by its subscript. of a substance is the sum of the average masses of the atoms in one molecule of a substance. It is calculated by adding together the atomic masses of the elements in the substance, each multiplied by its subscript (written or implied) in the molecular formula. Because the units of atomic mass are atomic mass units, the units of molecular mass are also atomic mass units. The procedure for calculating molecular masses is illustrated in Example 1.

Example 1.4.1

Calculate the molecular mass of ethanol, whose condensed structural formula is CH₃CH₂OH. Among its many uses, ethanol is a fuel for internal combustion engines.

Given: molecule

Asked for: molecular mass

Strategy:

A Determine the number of atoms of each element in the molecule.

B Obtain the atomic masses of each element from the periodic table and multiply the atomic mass of each element by the number of atoms of that element.

C Add together the masses to give the molecular mass.

Solution:

A The molecular formula of ethanol may be written in three different ways: CH₃CH₂OH (which illustrates the presence of an ethyl group, CH₃CH₂−, and an −OH group), C₂H₅OH, and C₂H₆O; all show that ethanol has two carbon atoms, six hydrogen atoms, and one oxygen atom.

B Taking the atomic masses from the periodic table, we obtain

( 2 times atomic; mass;of:carbon = 2;atoms left( {dfrac{12.011amu}{atom}} right) = 24.022;amu)

( 6 times atomic; mass;of:hydrogen = 6;atoms left( {dfrac{1.0079amu}{atom}} right) = 6.0474;amu)

( 1 times atomic; mass;of:oxygen = 1;atoms left( {dfrac{15.9994amu}{atom}} right) = 15.9994amu)​

C Adding together the masses gives the molecular mass:

24.022 amu + 6.0474 amu + 15.9994 amu = 46.069 amu

Alternatively, we could have used unit conversions to reach the result in one step, as described in Essential Skills 2

( left [ 2; atoms: ; left ( dfrac{12.011; amu}{1, ; atom; C} right ) right ] +)​ ( left [ 6; atoms: H; left ( dfrac{1.0079; amu}{1, ; atom; H} right ) right ]+) ( left [ 1; atoms: O; left ( dfrac{15.9994; amu}{1, ; atom; O} right ) right ] )

The same calculation can also be done in a tabular format, which is especially helpful for more complex molecules:

Exercise

Calculate the molecular mass of trichlorofluoromethane, also known as Freon-11, whose condensed structural formula is CCl₃F. Until recently, it was used as a refrigerant. The structure of a molecule of Freon-11 is as follows:

Answer: 137.368 amu

Note the Pattern

Atomic mass, and molecular mass have the same units: atomic mass units.

The Mole

Each chemical compound has a particular combination of atoms and the ratios of the numbers of atoms of the elements present are usually small whole numbers. The problem for early chemists was to discover the quantitative relationship between the number of atoms in a chemical substance and its mass. Because the masses of individual atoms are so minuscule (on the order of 10⁻²³ g/atom), chemists do not measure the mass of individual atoms or molecules. In the laboratory, for example, the masses of compounds and elements used by chemists typically range from milligrams to grams, while in industry, chemicals are bought and sold in kilograms and tons. To analyze the transformations that occur between individual atoms or molecules in a chemical reaction. A process in which a substance is converted to one or more other substances with different compositions and properties, it is therefore absolutely essential for chemists to know how many atoms or molecules are contained in a measurable quantity in the laboratory—a given mass of sample. The unit that provides this link is the mole (mol). The quantity of a substance that contains the same number of units (e.g., atoms or molecules) as the number of carbon atoms in exactly 12 g of isotopically pure carbon-12., from the Latin moles, meaning “pile” or “heap” (not from the small subterranean animal!).

Many familiar items are sold in numerical quantities that have unusual names. For example, cans of soda come in a six-pack, eggs are sold by the dozen (12), and pencils often come in a gross (12 dozen, or 144). Sheets of printer paper are packaged in reams of 500, a seemingly large number. Atoms are so small, however, that even 500 atoms are too small to see or measure by most common techniques. Any readily measurable mass of an element or compound contains an extraordinarily large number of atoms, molecules, or ions, so an extraordinarily large numerical unit is needed to count them. The mole is used for this purpose.

A mole is defined as the amount of a substance that contains the number of carbon atoms in exactly 12 g of isotopically pure carbon-12. According to the most recent experimental measurements, this mass of carbon-12 contains 6.022142 × 10²³ atoms, but for most purposes 6.022 × 10²³ provides an adequate number of significant figures. Just as 1 mol of atoms contains 6.022 × 10²³ atoms, 1 mol of eggs contains 6.022 × 10²³ eggs. The number in a mole is called Avogadro’s numberThe number of units (e.g., atoms, molecules, or formula units) in 1 mol: 6.022142 x 10²³, after the 19th-century Italian scientist who first proposed how to measure the number of molecules in a gas. Since the mass of the gas can also be measured on a sensitive balance, knowing both the number of molecules and their total mass allows us to simply determine the mass of a single molecule in grams.

The mole provides a bridge between the atomic world (amu) and the laboratory (grams). It allows determination of the number of molecules or atoms by weighing them. The numerical value of Avogadro's number, usually written as No, is a consequence of the arbitrary value of one kilogram, a block of Pt-Ir metal called the International Prototype Kilogram, and the choice of reference for the atomic mass unit scale, one atom of carbon-12. A mole of C-12 by definition weighs exactly 12 g and Avogadro's number is determined by counting the number of atoms. It is not so easy. Avogadro's number is the fundamental constant that is least accurately determined.

The definition of a mole—that is, the decision to base it on 12 g of carbon-12—is arbitrary but one arrived at after some discussion between chemists and physicists debating about whether to use naturally occurring carbon, a mixture of C-12 and C-13, or hydrogen. The important point is that 1 mol of carbon—or of anything else, whether atoms, compact discs, or houses—always has the same number of objects: 6.022 × 10²³.

In the following video, Prof. Steve Boon shows how Avogadro's hypothesis can be used to measure the molecular masses of He, N₂ and CO2. Follow along and record the measurements to get the relative masses. When we consider the behavior of gases in Unit 4, we can use the data to calculate the molecular weight of each gas. This method was, until the invention of the mass spectrometer, the best way of measuring molecular weights of gas molecules

Note the Pattern

One mole always has the same number of objects: 6.022 × 10²³.

To appreciate the magnitude of Avogadro’s number, consider a mole of pennies. Stacked vertically, a mole of pennies would be 4.5 × 10¹⁷ mi high, or almost six times the diameter of the Milky Way galaxy. If a mole of pennies were distributed equally among the entire population on Earth, each person would get more than one trillion dollars. Clearly, the mole is so large that it is useful only for measuring very small objects, such as atoms.

The concept of the mole allows us to count a specific number of individual atoms and molecules by weighing measurable quantities of elements and compounds. To obtain 1 mol of carbon-12 atoms, we would weigh out 12 g of isotopically pure carbon-12. Because each element has a different atomic mass, however, a mole of each element has a different mass, even though it contains the same number of atoms (6.022 × 10²³). This is analogous to the fact that a dozen extra large eggs weighs more than a dozen small eggs, or that the total weight of 50 adult humans is greater than the total weight of 50 children. Because of the way in which the mole is defined, for every element the number of grams in a mole is the same as the number of atomic mass units in the atomic mass of the element. For example, the mass of 1 mol of magnesium (atomic mass = 24.305 amu) is 24.305 g. Because the atomic mass of magnesium (24.305 amu) is slightly more than twice that of a carbon-12 atom (12 amu), the mass of 1 mol of magnesium atoms (24.305 g) is slightly more than twice that of 1 mol of carbon-12 (12 g). Similarly, the mass of 1 mol of helium (atomic mass = 4.002602 amu) is 4.002602 g, which is about one-third that of 1 mol of carbon-12. Using the concept of the mole, we can now restate Dalton’s theory: 1 mol of a compound is formed by combining elements in amounts whose mole ratios are small whole numbers. For example, 1 mol of water (H₂O) has 2 mol of hydrogen atoms and 1 mol of oxygen atoms.

Molar Mass

The molar massThe mass in grams of 1 mol of a substance. of a substance is defined as the mass in grams of 1 mol of that substance. One mole of isotopically pure carbon-12 has a mass of 12 g. For an element, the molar mass is the mass of 1 mol of atoms of that element; for a covalent molecular compound, it is the mass of 1 mol of molecules of that compound; for an ionic compound, it is the mass of 1 mol of formula units. That is, the molar mass of a substance is the mass (in grams per mole) of 6.022 × 10²³ atoms, molecules, or formula units of that substance. In each case, the number of grams in 1 mol is the same as the number of atomic mass units that describe the atomic mass, the molecular mass, or the formula mass, respectively.

Note the Pattern

The molar mass of any substance is its atomic mass, molecular mass, or formula mass in grams per mole.

The periodic table lists the atomic mass of carbon as 12.011 amu; the average molar mass of carbon—the mass of 6.022 × 10²³ carbon atoms—is therefore 12.011 g/mol:

The molar mass of naturally occurring carbon is different from that of carbon-12 and is not an integer because carbon occurs as a mixture of carbon-12, carbon-13, and carbon-14. One mole of carbon still has 6.022 × 10²³ carbon atoms, but 98.89% of those atoms are carbon-12, 1.11% are carbon-13, and a trace (about 1 atom in 10¹²) are carbon-14. Similarly, the atomic mass of uranium is 238.03 g/mol, and the atomic mass of iodine is 126.90 g/mol. When we deal with elements such as iodine and sulfur, which occur as a diatomic molecule (I₂) and a polyatomic molecule (S₈), respectively, molar mass usually refers to the mass of 1 mol of atoms of the element—in this case I and S, not to the mass of 1 mol of molecules of the element (I₂ and S₈).

The molar mass of ethanol is the mass of ethanol (C₂H₅OH) that contains 6.022 × 10²³ ethanol molecules. As you calculated in Example 1, the molecular mass of ethanol is 46.069 amu. Because 1 mol of ethanol contains 2 mol of carbon atoms (2 × 12.011 g), 6 mol of hydrogen atoms (6 × 1.0079 g), and 1 mol of oxygen atoms (1 × 15.9994 g), its molar mass is 46.069 g/mol. Similarly, the formula mass of calcium phosphate [Ca₃(PO₄)₂] is 310.177 amu, so its molar mass is 310.177 g/mol. This is the mass of calcium phosphate that contains 6.022 × 10²³ formula units.

The mole is the basis of quantitative chemistry. It provides chemists with a way to convert easily between the mass of a substance and the number of individual atoms, molecules, or formula units of that substance. Conversely, it enables chemists to calculate the mass of a substance needed to obtain a desired number of atoms, molecules, or formula units. For example, to convert moles of a substance to mass, we use the relationship

or, more specifically,

( molesleft ( dfrac{grams}{mole} right ) = grams )​

( left ( dfrac{mass}{molar; mass} right )rightarrow moles tag{1.4.2} )

( left ( dfrac{grams}{grams/mole} right )=gramsleft ( dfrac{mole}{grams} right )=moles )

Be sure to pay attention to the units when converting between mass and moles.

Figure 1.4.2 is a flowchart for converting between mass; the number of moles; and the number of atoms, molecules, or formula units. The use of these conversions is illustrated in Example 3 and Example 4.

Figure 1.4.2 A Flowchart for Converting between Mass; the Number of Moles; and the Number of Atoms, Molecules, or Formula Units

Example 1.4.2

For 35.00 g of ethylene glycol (HOCH₂CH₂OH), which is used in inks for ballpoint pens, calculate the number of

1. moles.
2. molecules.

Given: mass and molecular formula

Asked for: number of moles and number of molecules

Strategy:

A Use the molecular formula of the compound to calculate its molecular mass in grams per mole.

B Convert from mass to moles by dividing the mass given by the compound’s molar mass.

C Convert from moles to molecules by multiplying the number of moles by Avogadro’s number.

Solution:

A The molecular mass of ethylene glycol can be calculated from its molecular formula using the method illustrated in Example 1:

The molar mass of ethylene glycol is 62.068 g/mol

B The number of moles of ethylene glycol present in 35.00 g can be calculated by dividing the mass (in grams) by the molar mass (in grams per mole):

( ; 35.00; g; ethylene glycolleft ( frac{1; mol; ethylene; glycol; (g))}{62.068; g; ethylene; glycol} right )=0.5639; mol; ethylene; glycol)

It is always a good idea to estimate the answer before you do the actual calculation. In this case, the mass given (35.00 g) is less than the molar mass, so the answer should be less than 1 mol. The calculated answer (0.5639 mol) is indeed less than 1 mol, so we have probably not made a major error in the calculations.

C To calculate the number of molecules in the sample, we multiply the number of moles by Avogadro’s number:

( molecules; of; ethylene; glycol=0.5639; molleft ( dfrac{6.022times 10^{23}}{1; mol} right ) )

( = 3.396times 10^{23}; molecules​ )

Exercise

For 75.0 g of CCl₃F (Freon-11), calculate the number of

1. moles.
2. molecules.

Answer:

1. 0.546 mol
2. 3.29 × 10²³ molecules

Example 1.4.3

Calculate the mass of 1.75 mol of each compound.

1. S₂Cl₂ (common name: sulfur monochloride; systematic name: disulfur dichloride)
2. Ca(ClO)₂ (calcium hypochlorite)

Given: number of moles and molecular or empirical formula

Asked for: mass

Strategy:

A Calculate the molecular mass of the compound in grams from its molecular formula (if covalent) or empirical formula (if ionic).

B Convert from moles to mass by multiplying the moles of the compound given by its molar mass.

Solution:

We begin by calculating the molecular mass of S₂Cl₂ and the formula mass of Ca(ClO)₂.

A The molar mass of S₂Cl₂ is obtained from its molecular mass as follows:

The molar mass of S₂Cl₂ is 135.036 g/mol.

The mass of 1.75 mol of S₂Cl₂ is calculated as follows:

( moles; S{_{2}}Cl_{2} left [molar; mass dfrac{g}{mol} right ]= mass; S{_{2}}Cl_{2} )

( 1.75; mol; S{_{2}}Cl_{2}left ( dfrac{135.036; g; S{_{2}}Cl_{2}}{1;mol;S{_{2}}Cl_{2}} right )=236;g; S{_{2}}Cl_{2} )

B The formula mass of Ca(ClO)₂ is obtained as follows:

Molar Mass Of Elements Calculator

The molar mass of Ca(ClO)₂ is 142.983 g/mol

( moles; Caleft ( ClO right )_{2}left [ dfrac{molar; mass; Caleft ( ClO right )_{2}}{1; mol; Caleft ( ClO right )_{2}} right ]=mass; Caleft ( ClO right )_{2} )

( 1.75; mol; Caleft ( ClO right )_{2}left [ dfrac{142.983; g Caleft ( ClO right )_{2}}{1; mol; Caleft ( ClO right )_{2}} right ]=250.; g; Caleft ( ClO right )_{2} )​

Exercise

Calculate the mass of 0.0122 mol of each compound.

1. Si₃N₄ (silicon nitride), used as bearings and rollers
2. (CH₃)₃N (trimethylamine), a corrosion inhibitor

Answer:

1. 1.71 g
2. 0.721 g

Summary

The molecular mass and the formula mass of a compound are obtained by adding together the atomic masses of the atoms present in the molecular formula or empirical formula, respectively; the units of both are atomic mass units (amu). The mole is a unit used to measure the number of atoms, molecules, or (in the case of ionic compounds) formula units in a given mass of a substance. The mole is defined as the amount of substance that contains the number of carbon atoms in exactly 12 g of carbon-12 and consists of Avogadro’s number (6.022 × 10²³) of atoms of carbon-12. The molar mass of a substance is defined as the mass of 1 mol of that substance, expressed in grams per mole, and is equal to the mass of 6.022 × 10²³ atoms, molecules, or formula units of that substance.

Key Takeaway

• To analyze chemical transformations, it is essential to use a standardized unit of measure called the mole.

Conceptual Problems

1. Describe the relationship between an atomic mass unit and a gram.

2. Construct a flowchart to show how you would calculate the number of moles of silicon in a 37.0 g sample of orthoclase (KAlSi₃O₈), a mineral used in the manufacture of porcelain.

3. Construct a flowchart to show how you would calculate the number of moles of nitrogen in a 22.4 g sample of nitroglycerin that contains 18.5% nitrogen by mass.

Numerical Problems

1. Derive an expression that relates the number of molecules in a sample of a substance to its mass and molecular mass.

2. Calculate the molecular mass or formula mass of each compound.

   1. KCl (potassium chloride)
   2. NaCN (sodium cyanide)
   3. H₂S (hydrogen sulfide)
   4. NaN₃ (sodium azide)
   5. H₂CO₃ (carbonic acid)
   6. K₂O (potassium oxide)
   7. Al(NO₃)₃ (aluminum nitrate)
   8. Cu(ClO₄)₂ [copper(II) perchlorate]

3. Calculate the molecular mass or formula mass of each compound.

   1. V₂O₄ (vanadium(IV) oxide)
   2. CaSiO₃ (calcium silicate)
   3. BiOCl (bismuth oxychloride)
   4. CH₃COOH (acetic acid)
   5. Ag₂SO₄ (silver sulfate)
   6. Na₂CO₃ (sodium carbonate)
   7. (CH₃)₂CHOH (isopropyl alcohol)

4. Calculate the mass in grams of each sample.

   1. 0.520 mol of N₂O₄
   2. 1.63 mol of C₆H₄Br₂
   3. 4.62 mol of (NH₄)₂SO₃

5. Give the number of molecules or formula units in each sample.

   1. 1.30 × 10⁻² mol of SCl₂
   2. 1.03 mol of N₂O₅
   3. 0.265 mol of Ag₂Cr₂O₇

6. Give the number of moles in each sample.

   1. 9.58 × 10²⁶ molecules of Cl₂
   2. 3.62 × 10²⁷ formula units of KCl
   3. 6.94 × 10²⁸ formula units of Fe(OH)₂

7. What is the total number of atoms in each sample?

   1. 0.431 mol of Li
   2. 2.783 mol of methanol (CH₃OH)
   3. 0.0361 mol of CoCO₃
   4. 1.002 mol of SeBr₂O

8. What is the total number of atoms in each sample?

   1. 0.980 mol of Na
   2. 2.35 mol of O₂
   3. 1.83 mol of Ag₂S
   4. 1.23 mol of propane (C₃H₈)

9. What is the total number of atoms in each sample?

   1. 2.48 g of HBr
   2. 4.77 g of CS₂
   3. 1.89 g of NaOH
   4. 1.46 g of SrC₂O₄

10. Decide whether each statement is true or false and explain your reasoning.

    1. There are more molecules in 0.5 mol of Cl₂ than in 0.5 mol of H₂.
    2. One mole of H₂ has 6.022 × 10²³ hydrogen atoms.
    3. The molecular mass of H₂O is 18.0 amu.
    4. The formula mass of benzene is 78 amu.

11. Complete the following table.

    Substance	Mass (g)	Number of Moles	Number of Molecules or Formula Units	Number of Atoms or Ions
    MgCl2	37.62
    AgNO3	2.84
    BH4Cl	8.93 × 1025
    K2S	7.69 × 1026
    H2SO4	1.29
    C6H14	11.84
    HClO3	2.45 × 1026

Contributors

• Anonymous

Modified by Joshua Halpern, Scott Sinex and Scott Johnson

Molar Mass Of Elements On The Periodic Table

Verifying Avogadro's Hypothesis Video from HC Communications on YouTube